y=4^{log₂ x}, prove that dy/dx=2x

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{y}=4^{{\log }_2\left(\mathrm{x}\right)} \\ \Rightarrow \mathrm{y}=2^{2{\log }_2\left(\mathrm{x}\right)} \\ \Rightarrow \mathrm{y}=2^{{\log }_2\left({\mathrm{x}}^2\right)} \left[\mathrm{As} \mathrm{n}·\log \left(\mathrm{m}\right)=\log \left({\mathrm{m}}^{\mathrm{n}}\right)\right] \\ \Rightarrow \mathrm{y}={\mathrm{x}}^2 \left[\mathrm{As} {\mathrm{a}}^{{\log }_{\mathrm{a}}\mathrm{M}}=\mathrm{M}\right] \\ \Rightarrow \frac{\mathbf{dy}}{\mathbf{dx}}\mathbf{=}\mathbf{2}\mathbf{x} \end{gathered}$$

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